In this paper, a stabilization scheme for a class of continuous-time nonlinear Markov jump systems is investigated by sampled-data control mechanism. This stabilization scheme is given in the form of a discrete-time state feedback controller which is designed based on the approximate discrete-time model (ADTM) of the original continuous-time system via the discrete-time design method. During the process of controller design, an appropriate iteration step size is selected for the ADTM to restore the missing intersampling data due to the sampling characteristics, and this provides the iteration solutions of ADTM to the controller. The introduction of the iteration step size achieves a perfect tradeoff between calculation precision and control cost which not only guarantees the calculation precision of the ADTM, but also reduces sampling frequency effectively. Subsequently, we analyze the consistency condition between the continuous-time nonlinear Markov jump systems and its ADTM, and give the criterion of the mean-square exponential stability of the system. Based on this criterion, we prove the mean-square exponential stability of the closed-loop sampled-data system with the designed discrete-time state feedback controller. Finally, the feasibility and effectiveness of this scheme are clearly verified by a numerical example.

中文翻译：

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基于近似离散时间模型的一类连续时间非线性马尔可夫跳跃系统的镇定

本文通过采样数据控制机制研究了一类连续时间非线性马尔可夫跳跃系统的镇定方案。该镇定方案以离散时间状态反馈控制器的形式给出，该控制器是基于原始连续时间系统的近似离散时间模型（ADTM）通过离散时间设计方法设计的。在控制器设计过程中，为ADTM选择合适的迭代步长来恢复由于采样特性而丢失的互采样数据，从而为控制器提供ADTM的迭代解决方案。迭代步长的引入实现了计算精度和控制成本的完美平衡，既保证了ADTM的计算精度，还能有效降低采样频率。随后，我们分析了连续时间非线性马尔可夫跳跃系统与其ADTM之间的一致性条件，并给出了系统均方指数稳定性的判据。基于此准则，我们证明了具有设计的离散时间状态反馈控制器的闭环采样数据系统的均方指数稳定性。最后，通过数值算例清楚地验证了该方案的可行性和有效性。我们用设计的离散时间状态反馈控制器证明了闭环采样数据系统的均方指数稳定性。最后，通过数值算例清楚地验证了该方案的可行性和有效性。我们用设计的离散时间状态反馈控制器证明了闭环采样数据系统的均方指数稳定性。最后，通过数值算例清楚地验证了该方案的可行性和有效性。